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Find the greatest number which divides 2011 and 2423 leaving remainders 9 and 5 respectively?
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Find the greatest number which divides 2011 and 2423 leaving remainder...


The greatest number that divides 2011 and 2423 leaving remainders 9 and 5 respectively can be found by using the concept of the Chinese Remainder Theorem.
- Step 1: Finding the divisors
To find the divisors that leave remainders 9 and 5 when divided by 2011 and 2423 respectively, we subtract the remainders from the numbers:
For 2011: 2011 - 9 = 2002
For 2423: 2423 - 5 = 2418
- Step 2: Finding the greatest common divisor
Next, we find the greatest common divisor of 2002 and 2418 using Euclid's algorithm:
2418 = 2002 * 1 + 416
2002 = 416 * 4 + 186
416 = 186 * 2 + 44
186 = 44 * 4 + 10
44 = 10 * 4 + 4
10 = 4 * 2 + 2
4 = 2 * 2
The greatest common divisor of 2002 and 2418 is 2.
- Step 3: Conclusion
Therefore, the greatest number that divides 2011 and 2423 leaving remainders 9 and 5 respectively is 2.
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Find the greatest number which divides 2011 and 2423 leaving remainders 9 and 5 respectively?
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